How does the manual PTO clutch work.?
 

Can someone explain exactly how the mechanical clutch on my 147 works?

Everything on the crank appears to be mounted solid. Nothing freewheels or slides. Both the starter and mower pulleys turn at the same time.

When you push foreword on the engagement lever what exactly is suppose to happen.?

When you push forward on engagement lever, you are engaging the PTO. When the clutch is engaged, the thrust button on the lever arm in front of PTO does not touch the PTO button. There is a small gap between the buttons.... refer to the following link on mechanical PTOs.

https://www.onlycubcadets.net/forum/showthread.php?t=9

My clutch seems to be "engaged like it sits. Both pulleys rotate at the same time.

Then it's probably rusted tight or not adjusted at all.
Is there even a button present on the engagement lever in front of the PTO?
Time to remove and repair.

The pulleys will rotate if you do not have a belt on it. Pictures of what you got will help.

If everything is adjusted and operating correctly:
!. When the handle/lever is in the forward (engaged) position, the springs "D" provide pressure to sandwich the disc "C" between two plates, one of which is the belt pulley.
2. Becaust the other plate is attacched to the motor crankshaft, the belt pulley will spin with the motor.
3. When the handle/lever is pulled back (dis-engaged) button "A" presses on button "B" and relieves the pressure of the springs "D" allowing the belt pulley to freewheel, (or float) on its bearing and not turn with the motor.

Hope that makes cents 2u.

I think d spring relieves the plates apart. That black pry bar shaped thing down by b provides the spring tension to the arms bolts and holds the plates together to drive disc c, which is connected via the basket pulley lugs to the crank.

Pulling the lever back pushes the button and takes the pressure off the arms.